My guess is that Dreamhost had the database optimized for multiple users and high performance, while you're probably just using mysql out of the box with no tweaking. I recommend checking out and learning the excellent mysqlreport to tweak your mysql server. Also, is the database at DH running on a separate physical machine, or the same one as your Rails account? Giving the database its own machine will invariably improve performance a lot compared to running it on the same machine as the application it's serving.
If Dreamhost's mysql is running on the same physical machine, you might be able to steal a copy of their my.cnf to compare it with the one you're using at Slicehost. Just cp /etc/mysql/my.cnf to your home directory and compare it with the one on your slice.